Using a
new general approach to limits in optical structures that counts
orthogonal waves generated by scattering, we derive an upper limit to
the number of bits of delay possible in one-dimensional slow light
structures that are based on linear optical response to the signal
field. The limit is essentially the product of the length of the
structure in wavelengths and the largest relative change in dielectric
constant anywhere in the structure at any frequency of interest. It
holds for refractive index, absorption or gain variations with arbitrary
spectral or spatial form. It is otherwise completely independent of the
details of the structure’s design, and does not rely on concepts of
group velocity or group delay.